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The radius of the satellite’s orbit around the center of the Earth is r = 17 2 R , where R is the radius of the Earth. Hint: You may find it useful to take into account that the gravitational force is a conservative force. Hint: The universal gravitational force law is F~ = G M m r 2 ˆr . Earth R Satellite 17 2 R Caution: Neglect the rotational kinetic energy due to the Earth’s rotation. Find the energy required to launch a satellite from Earth into the circular orbit at the specified radius r = 17 2 R.

Respuesta :

Answer:

[tex]E = \frac{15GMm}{17R}[/tex]

Explanation:

The potential energy of the satellite at the surface of the Earth is:

[tex]U_i = -\frac{GMm}{R}[/tex]

The potential energy of the satellite in the circular orbit is:

[tex]U_f=-\frac{GMm}{17/2 R}[/tex]

The energy required to put the satellite in the orbit is the difference between the two potential energies:

[tex]E=U_f-U_i =-\frac{GMm}{R}(\frac{2}{17}-1)\\E = \frac{15GMm}{17R}[/tex]

The energy required to launch a satellite from Earth into the circular orbit at the specified radius should be E = 15 GMm/ 17R.

calculation of the energy required:

We know that

The potential energy of the satellite at the surface of the Earth is

U_i = -GMm/R

And,

The potential energy of the satellite in the circular orbit should be

U_f = -GMm/ 17/2R

So here the energy required should be

= 15GMm/17R

hence, The energy required to launch a satellite from Earth into the circular orbit at the specified radius should be E = 15 GMm/ 17R.

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